Math Help - Common factor help

1. Common factor help

Need some help on a easy question that i can't remenber how to do it
$\frac{1}{7^{3^{n+1}}} + \frac{1}{7^{3^{n+2}}} + ...$
$\frac{1}{7^{3^{n+1}}} (1+ \frac{1}{7^{x}} + ...)$

What should $x$ be?

Thank you

2. Originally Posted by kleenex
Need some help on a easy question that i can't remenber how to do it
$\frac{1}{7^{3^{n+1}}} + \frac{1}{7^{3^{n+2}}} + ...$
$\frac{1}{7^{3^{n+1}}} (1+ \frac{1}{7^{x}} + ...)$

What should $x$ be?

Thank you
We need to satisfy $\frac{1}{7^{3^{n+1}}}\cdot \frac{1}{7^x} = \frac{1}{7^{3^{n+2}}}$.
Thus, $7^{3^{n+1}}\cdot 7^x = 7^{3^{n+2}}$
Thus, $3^{n+1} + x = 3^{n+2}$.